-16t^2+42t+144=126

Solution for -16t^2+42t+144=126 equation:

Simplifying
-16t2 + 42t + 144 = 126

Reorder the terms:
144 + 42t + -16t2 = 126

Solving
144 + 42t + -16t2 = 126

Solving for variable 't'.

Reorder the terms:
144 + -126 + 42t + -16t2 = 126 + -126

Combine like terms: 144 + -126 = 18
18 + 42t + -16t2 = 126 + -126

Combine like terms: 126 + -126 = 0
18 + 42t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 21t + -8t2) = 0

Factor a trinomial.
2((3 + -1t)(3 + 8t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Subproblem 2
Set the factor '(3 + 8t)' equal to zero and attempt to solve:

Simplifying
3 + 8t = 0

Solving
3 + 8t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 8t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8t = 0 + -3
8t = 0 + -3

Combine like terms: 0 + -3 = -3
8t = -3

Divide each side by '8'.
t = -0.375

Simplifying
t = -0.375
Solution
t = {3, -0.375}